Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Living_dreams
Group Title
find all local max,min and/or saddle point of f(x,y)=4+x^3+y^3xy
 2 years ago
 2 years ago
Living_dreams Group Title
find all local max,min and/or saddle point of f(x,y)=4+x^3+y^3xy
 2 years ago
 2 years ago

This Question is Closed

Avva Group TitleBest ResponseYou've already chosen the best response.0
would you plz write the function using equation
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
hmm, something to do with:\[f_{xy}f_{yx}(f_{xx})^2\] or did i recall that incorrectly?
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
almost had it :) \[f_{xx}f_{yy}(f_{xy})^2\]
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
\[4+x ^{3}+y ^{3}3xy\]
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
it fxx.fyy(fxy)^2
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
i jst want to verify the answer for it !
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
what answer did you get?
 2 years ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
\[fx = 2x3y \] \[fy= 2y3x\] on solving both equations the point is (0,0) \[fxx = 2\] , \[fyy= 2\] \[fxy = \] \[D = 5 <0 saddle point\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
that's not quite right I don't think
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[f(x,y)=4+x^3+y^33xy\]\[f_x=3x^23y=0\implies y=x^2\]\[f_y=3y^23x=3x^43x=3x^3(x1)=0\]\[ x=\{0,1\},y=\{0,1\}\]
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
its x^3 so i have (0,0) ,(1,1)and a (1,1) i am not sure if (1,1) should be there oor not
 2 years ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
@Living_dreams I solved what you mentioned in your comment
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
there is no x=1 solution, I don't see how you get that
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
@Avva I don't see how you get your fx and fy
 2 years ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
Ooh I saw the powers on X ^ y 2 not 3
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@Avva thanks for ur help but i was wonder abt the max and min points! n\ @TuringTest : 3y^23x=0 i sub y=x^2 from other equation so it will be 3x(x^31)=0 therefore you have x =0,1,1 i am not sure abt 1 though !! tht was my question
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
x^3=1 does not have x=1 as a solution since (1)^3=1, not 1
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I did screw up my factoring earlier though, you were right about that :P
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
3x(x^31)=0 3x=0 > x=0 x^3=1 > x=1
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@TuringTest that alrite!! :) so now my question is x^3=1 so will i hv x=1 if i solve for x ?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
no, again, because \((1)^3\neq1\) so \(x^3=1\) has only one real solution, x=1 x=1 is NOT a solution
 2 years ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
the other two roots are complex not real
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@TuringTest oh ok thanks a lot for ur help!! so the final ans will be (0,0 ) is a saddle point and (1,1) will be a local minimum !
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
exactly :)
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@Avva :thanks for ur help !! :)
 2 years ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
@Living_dreams URW :) sorry I didn't get that the powers are 3 at first
 2 years ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
it okay !!i knw it get hard to tell the difference between 2 and 3 if we type it in equation form !!
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.